That is a great idea - you may find that if the water has a lot of CO2
in it, it will outgas overnight and the pH drops. Check your KH
too, as this goes hand in hand with pH.
If your tap pH is still measuring high, then my next question is how old is the tank? Over time acidification will naturally occur, dropping the pH. As long as you don't do any drastic water changes all at once it should not be a problem, as long as it is stable. If you have a KH
of at least 3-4 degrees then it should keep your pH steady. However, it would take years for the pH to drop that many points from acidification.